Problem: Rewrite as a simplified fraction. ${0.\overline{95} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 95.9595...\\ 1x &= 0.9595...\end{aligned}}$ Subtracting the two equations, we have: ${99x = 95}$ ${x = \dfrac{95}{99}} $